Trading group theory for randomness
- L. Babai
- MathematicsSymposium on the Theory of Computing
- 1 December 1985
The aim of this paper is to replace most of the (proven and unproven) group theory of [BS] by elementary combinatorial arguments and defines a new hierarchy of complexity classes “just above <italic>NP</italic””, introducing Arthur vs. Merlin games and proving that it consists precisely of those languages which belong to NP.
On Lovász’ lattice reduction and the nearest lattice point problem
- L. Babai
- Mathematics, Computer ScienceComb.
Answering a question of Vera Sós, we show how Lovász’ lattice reduction can be used to find a point of a given lattice, nearest within a factor ofcd (c = const.) to a given point in Rd. We prove that…
A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem
Checking computations in polylogarithmic time
- L. Babai, L. Fortnow, L. Levin, M. Szegedy
- Computer ScienceSymposium on the Theory of Computing
- 3 January 1991
WJe show that every nondeterministic computational task S(Z, y), defined as a polynomial time relation between the instance x, representing the input and output combined, and the witness y can be modified to a task S such that each instance/witness pair becomes checkable in poly!ogariihmic Monte Carlo time.
Canonical labeling of graphs
An algebraic approach to the problem of assigning canonical forms to graphs by computing canonical forms and the associated canonical labelings in polynomial time is announced.
Complexity classes in communication complexity theory
- L. Babai, P. Frankl, Janos Simon
- Computer Science27th Annual Symposium on Foundations of Computer…
- 27 October 1986
The main objective is to exploit the analogy between Turing machine (TM) and communication complexity (CC) classes to provide a more amicable environment for the study of questions analogous to the most notorious problems in TM complexity.
Non-deterministic exponential time has two-prover interactive protocols
It is shown that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time and that to prove membership in languages inEXP, the honest provers need the power ofEXP only.
The hardness of approximate optima in lattices, codes, and systems of linear equations
- Sanjeev Arora, L. Babai, J. Stern, E. Sweedyk
- Computer ScienceProceedings of IEEE 34th Annual Foundations of…
The Nearest Lattice Vector Problem (in any l/sub p/ norm), the Nearest Code-word Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems are proved.
Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes